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A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logo(XY)=logo(x)+logo(y). (x y) = log b (x) + log b
A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logo(XY)=logo(x)+logo(y). (x y) = log b (x) + log b
When we take the logarithm of both sides of ELN(XY)=ELN(x)+LN(y), we obtain LN(ELN(XY))=LN(ELN(x)+LN(y)). The logarithms and exponential cancel each other out (equation (4)), giving our product rule for logarithms, LN(XY)=LN(x)+LN(y).
0:24 5:03 Suggested clip Sum of logarithms with same base | Logarithms | Algebra II | Khan YouTubeStart of suggested client of suggested clip Sum of logarithms with same base | Logarithms | Algebra II | Khan
0:00 0:51 Suggested clip Learn how to condense natural logs separated by subtraction YouTubeStart of suggested client of suggested clip Learn how to condense natural logs separated by subtraction
log 100 = 2. Because. 102 = 100. This is an example of a base-ten logarithm. Log2 8 = 3. Because. 23 = 8. In general, you write log followed by the base number as a subscript. Log. Log a = r. LN. LN a = r.
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